Reliable Emergency Evacuation Route Planning Under Road Capacity Uncertainty

China is a country prone to natural disasters and other accidents,so it is urgent to establish and improve the national emergency management system and enhance the response capacity.Among them,how to effectively reduce the loss caused by the disaster is the key research direction of emergency evacuation.It is an effective means for decision-makers of relevant government departments to formulate a reliable and effective evacuation plan before the occurrence of disasters in order to deal with the evacuation of people according to the plan when disasters occur.The reliability of evacuation scheme is often related to the accuracy of the estimation of possible scenarios after the occurrence of disasters.However,due to the scarcity of disaster event data,it is very difficult to obtain accurate estimation.Therefore,how to make full use of limited data to make a reliable emergency evacuation plan,in order to quickly respond to the occurrence of disasters,is an urgent problem to be solved at present.In recent years,the problem of emergency evacuation path planning under the influence of various uncertain factors has been widely concerned,but most of them assume that the road capacity is a known constant and carry out analysis under the uncertain conditions of other parameters（such as demand）.However,road capacity plays a very important role in emergency evacuation path planning,and ignoring its uncertainty has a significant impact on the reliability of planning scheme.Recently,some scholars have begun to pay attention to the emergency evacuation path planning model with uncertain capacity.However,the basic assumption of their research is the exact probability distribution function of known capacity,such as the assumption of discrete probability distribution,uniform distribution,symmetric distribution,Weibull distribution,etc.All of these studies assume that the decision maker gives the optimal evacuation path planning scheme at the stage of formulating emergency evacuation planning scheme,that is,before the disaster occurs,the decision maker completely knows the accurate information（or accurate value or accurate probability distribution）of road capacity after the disaster occurs.If the actual road capacity conforms to the hypothesis after the disaster occurs,the planning scheme designed thereby will produce better results.However,if the actual road capacity is greatly different from the assumptions,the proposed planning scheme may lose its optimality,resulting in road congestion,and ultimately lead to the unreliability of the scheme.In this paper,we assume that the probability distribution of road capacity cannot be accurately obtained,and only part of the characteristic information of the probability distribution is known,and the method of distributionally robust optimization is used for modeling analysis.The method first build uncertainty is characterized by the known information of the distribution function sets（Ambiguity set）,and then based on the uncertainty set,determine the worst case to achieve optimal evacuation path planning scheme,so can avoid the existing research on the disadvantages of probability distribution assumption too road capacity,to ensure the reliability of the emergency evacuation planning.In addition,most of the previous literature studies on evacuation network traffic allocation are based on Wardrop’s first or second principle to determine the optimal total evacuation time.Wardrop’s first principleis that all evacuees follow the objective of "minimizing the total network travel time" to select the route,while the second principlemeans that the traffic flow on the congested network should be allocated according to the minimum average or total travel cost,so that the designer of evacuation plan should minimize the movement time of the total network.When the emergency evacuation path planning is made,the disaster has not occurred,and the actual specific situation is uncertain.Therefore,the evacuation path will have a certain probability of traffic congestion,which is not considered in Wardrop’s two models.Based on this fact,this article uses Kerner’s Breakdown Minimization Principle（BM）.The purpose of the BM traffic allocation principle is to allocate link traffic to minimize the probability of traffic congestion,thus ultimately affect the decision and implementation of the entire evacuation plan,and therefore ensure the reliability of evacuation plan.The main research contents and works of this paper are as follows:（1）Considering the emergency evacuation path planning problem with uncertain road capacity but known partial distribution information,the importance of congestion in emergency evacuation path planning is emphasized,and the reliability goal of minimizing the possibility of congestion is used to measure the emergency evacuation scheme.The corresponding distributionally robust chance constrained decision model is constructed by using several methods such as distributionally robust optimization,and the model is transformed and derived.Then,the software was used to solve the final optimization model,and the corresponding evacuation planning scheme was obtained,and the Compare Determination Algorithm was designed.The effectiveness of the model and the reliability of evacuation scheme were verified by numerical simulation.（2）Considering both the road capacity and the uncertainty of the demand of evacuees between each source node,only part of the distribution information is known,and the model is modeled using the distributionally robust optimization.Focusing on the nonindependence of the number of evacuees between each source node due to various factors,a corresponding distributionally robust chance constrained model is established,and the reduction method is used to deal with it.Finally,the evacuation scheme is obtained by solving the final optimization model,and the reliability of the obtained evacuation scheme and the validity of the model method are determined through the comparison of the design.The results of the final simulation experiments verify that the proposed model has good performance.（3）On the basis of the uncertain model of road capacity,the significant influence of road stability coefficient on the actual capacity of post-disaster roads was emphasized,and the optimization of emergency evacuation path planning was considered.In this paper,the concept of "stability coefficient" is proposed for the first time.Considering that the stability coefficient affecting road capacity is uncertain and its specific distribution is unknown in disaster scenarios,the emergency evacuation scheme planning problem with only partial distribution information of stability coefficient is studied.Finally,an approximate optimization model is obtained by establishing and solving the distributionally robust chance constrained model of the problem,and numerical experiments are carried out to prove the superiority of constructing the emergency evacuation path planning problem model using this method.